Method of detecting the orientation of an object in an image

ABSTRACT

A method of detecting the orientation of a radiographic image represented by a digital signal representation wherein mathematical moments of the digital signal representation are calculated relative to different reference entities and wherein a decision on the orientation of the radiographic image, for example the position of the thorax edge in a mammographic image, is obtained on the basis of an extreme value (minimum, maximum) of the calculated moments.

This application claims the benefit of and the priority to U.S.Provisional Patent Application No. 60/450,857 filed Feb. 27, 2003, andto European Patent Application No. 03100375.9 filed Feb. 19, 2003, bothof which are incorporated by reference.

FIELD OF THE INVENTION

The present invention relates to a method for detecting the orientationof object shapes in radiation images.

BACKGROUND OF THE INVENTION

In radiological practice, it is common to display different exposurespertaining to a patient study in a predefined format. This feature isknown as a hanging protocol. In film-based operation, it means that theradiologist or operator hangs the films on the light box in a specificspatial arrangement according to standard or local preferences.Determination of the orientation or reflection of an examination type,or verification of it when it is available, is beneficial to the correctdisplay of many examination types.

In screening mammography standard 4-views of left and right breast aretaken for each of the incidence directions (cranio-caudal (CC) andmedio-lateral oblique (MLO)). These views are typically displayed in amirrored fashion, such that the thorax edges or both breasts are centraland touching, and the left breast image being displayed on the right andthe right breast image being displayed on the left. However, becauseboth breasts images are acquired in a similar manner, and it is ingeneral not known which image is either corresponding to the left or theright breast, one image must be flipped before it can be positionedadjacent to the other image. In conventional screen-film imaging, X-rayopaque lead letters are radiographed simultaneously (RCC, LCC, RMLO andLMLO) with the object, and the RCC resp. RMLO films are flipped manuallyprior to hanging them on the right of the LCC resp. LMLO on the lightbox.

Digitally acquired mammograms may still be read in a conventional way byprinting them on film and displaying them on a light box. Pairs ofmammograms (e.g. the RCC/LCC pair and the RMLO/LMLO pair) may be printedon a single large film sheet or on two smaller sized sheets. Generally,the print margin of a hardcopy machine is adjustable, so as to minimizethe non-printed portion of an image. For mammography hardcopy, the printmargin corresponding to the thorax side is kept as small as possible, sothat a right-left pair of images, when viewed simultaneous and in closevicinity, shows a minimal non-diagnostic viewing area in between bothimages. Therefore, when using a pair of small sheets to print left andright image respectively, means to identify the thorax sideautomatically prior to printing them is needed, because the thorax sideposition is generally not known or it may not be assumed to be known.Likewise, in the large film option, where both images are printed on onefile sheet in order to compose the image such that the right image istouching in a mirroring manner to the left image, knowledge of thethorax side of both images is needed as well.

Digital mammography may be read on a computer display or viewing stationwithout having resort to printed mammograms, a viewing condition knownas softcopy reading. However, also here, the sub-examination typesidentifying right and left images may not be known at display time.Furthermore, the thorax edge orientation may not be standardized, e.g.it may either touch the left or right or the upper or lower imageborder. Hence, there is a need to accomplish the mirrored viewingdisposition in an automated way.

Generally, a hanging protocol function enables users to arrange anddisplay images on medical viewing stations to suit specific viewingpreferences. To this purpose, the sub-examination is used to assign thesub-images pertaining to a patient study of a body part to a position ina preferred display layout of that examination type. When the imagesub-type is known, hence its position in the layout is determined, theimage can still be oriented in 8 different ways: it can be orientedcorrectly, or it can be rotated of 90, 180 or 270 degrees; in any ofthese four cases, the image can also be flipped around a vertical (orhorizontal axis). Therefore, there is a need to derive the orientationof the image automatically, to assure viewing according to theradiological standard or local preferences.

WO 02/45437 discloses a method of determining orientations of digitizedradiographic images such as mammographic images from marker images (e.g.lead marker images). The digitized radiographic images are thendisplayed in a predetermined orientation and order.

In the article “Two dimensional shape and texture qunatification’,Bankman I., Spisz T. S., Pavlopoulos S., Handbook of Medical Imaging,Chapter 14, pages 215-230, XP002249040, Bankman Isaac N., editor,Academic Press, 2000, a method has been described for defining theorientation of an object in an image. More particularly the directionalong which an object is most elongated relative to a preferentialdirection such as a vertical axis is determined by calculating an angleθ in the calculation of which mathematical moment is used.

SUMMARY OF THE INVENTION

The above-mentioned objects are achieved by a method of detecting theorientation of a radiographic image represented by a digital signalrepresentation as set out in claim 1.

To detect the orientation of a radiographic image mathematical momentsare calculated relative to different reference entities (axes, points .. . ) and the orientation is derived from an extreme value of thesemathematical moments. By the term extreme value is meant maximum orminimum value, depending on the sign of the power of the spatialcoordinate function in the calculated moment as will be explainedfurther on.

In the context of the present invention the term orientation of an imagecan be defined on the basis of the image content. For example withregard to mammographic images the orientation of an image can be definedin terms of the position of the thorax edge or the position of nipplerelative to one of the image borders.

According to the present invention the orientation of a radiographicimage represented by a digital signal representation such as a functionf(x,y) is derived from the result of a calculation of at least onemathematical moment of the function f(x,y).

Another aspect of the present invention relates to a method of orientingan image into a predefined orientation. The method in general comprisesthe steps of (1) deriving the actual orientation of the image from itsdigital representation and (2) manipulating the image (e.g. by rotating,mirroring etc.) so that the envisioned orientation is obtained.

For the application of orienting an image into a predefined orientation,a geometric transformation can be applied to the image. The geometrictransformation is determined by the geometric parameters of the actualorientation and the envisioned orientation. Techniques known in theprior art for determining the geometric displacement field and theintensity interpolation can be used to geometrically modify the image tothe envisioned target orientation.

Specific features for preferred embodiments of the invention are set outin the dependent claims.

Further advantages and embodiments of the present invention will becomeapparent from the following description and accompanying drawings.

A specific aspect of the present invention relates to a computer programproduct adapted to carry out the method as set out in the claims whenrun on a computer.

Another specific aspect relates to a computer readable medium such as aCR-ROM comprising computer executable program code adapted to carry outthe method set out in the claims.

The method of the current invention is particularly suited in the fieldof digital mammography, to detect the thorax to nipple direction andfurther to align a left-right pair of breast views such that theirthorax sides are touching when printed on film or displayed on screen.

The invention is however not limited to this application.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart illustrating a method to manipulate a radiationimage according to the shape of objects in the diagnostic region(s) ofthe image,

FIG. 2 illustrates the method of determining the orientation of thebreast mass in CC views,

FIG. 3 illustrates the method of determining the orientation of thebreast mass in MLO views.

DETAILED DESCRIPTION OF THE INVENTION

A general overview of a method to manipulate a radiation image accordingto the shape of objects in the diagnostic region(s) of the image isgiven in FIG. 1.

Image Input:

In order to conduct a topological analysis of the mammography image toinfer the position of the breast's thorax side and the orientation ofthe nipple, shape analysis is performed.

Shape analysis is generally carried out starting from an intermediaterepresentation of an image typically involving the segmented imageand/or special shape descriptors.

A radiation image typically consist of three different areas:

-   -   The diagnostic area comprises pixels corresponding to patient        anatomy. In general, the outline of this imaged area may take        any shape.    -   The direct exposure area is the image region that has received        un-attenuated radiation. Although this region has constant        intensity corrupted by noise only, inhomogenities in incident        energy (e.g. X-ray source Heel effect) and receptor (e.g.        varying storage phosphor sensitivity in computed radiography)        may distort this pattern. In European patent application 1 256        907 a method is disclosed to estimate these global        inhomogenities retrospectively from the diagnostic image and        flatten the response in all image parts in accordance with an        extrapolated background signal.    -   The collimated areas appear on the image as highly attenuated        pixels. The shape of these areas typically is rectilinear, but        circular or curved collimation shapes may be applied as well.

Three different area transition types may be considered in a radiationimage: diagnostic/direct exposure, diagnostic/collimated area, anddirect exposure/collimated area boundaries.

Image Segmentation:

Segmentation algorithms aim at detecting and separating of the set ofpixels that constitute the object(s) under analysis. These techniquesmay be broadly classified according to the type of processing applied tothe image. Region-based algorithms group pixels in the image accordingto suitable similarity criteria. In European patent application EP 887769 a region-based algorithm is disclosed to segment direct exposureareas by grouping pixels according to centroid clustering of the grayvalue histogram. Edge based algorithms separate image pixels in highcontrast regions in the image according to gray value differences ofneighboring regions. In European patent application 610 605 and Europeanpatent application 742 536 an edge-based algorithm is disclosed todetect and delineate the boundaries between collimated areas anddiagnostic areas on a single or multiply exposed image. Either inregion-based and edge-based approaches, models may be used to restrictthe appearance or shape of the segmented image areas to obey predefinedphotometric or geometric constraints. An example of this paradigm arethe so-called Active Appearance and Active Shape Models (AAM and ASM).

Shape Analysis:

As a consequence of the segmentation result being either a region or aregion transition, shape analysis techniques may also be divided roughlyin either region-based or edge based procedures. Shape analysistechniques generally depart from a suitable representation of regionsand region boundary, and hence they may also broadly be divided inregion-based and contour-based classes. Examples of representations ofeither type are given in the sequel.

Shape analysis techniques are typically selected in view of the problemrequirements. These requirements will broadly fall in one of twoclasses. The first class may be termed topology problems, in that theproblem is one of locating and substantiating the specific spatialarrangement of an object shape with respect to other objects orreference systems. The second class may be termed characterization, andis closely linked with classification. In this problem class, shapespecific descriptors must be applied, and in general atopology-independent characterization is needed. Both problem classesare closely linked, because when the topology of a specific shape needsbe calculated, the shape must first be searched for and detected on thebasis of the shape's specific characteristics. Conversely, when thecharacteristics of a specific shape need be determined e.g. in order toclassify it, the shape must first be located in the image, which problemcomponent is one of topology. Given the topology and characteristics ofthe shape, the application specific problem can be solved.

Shape Description:

The result of a shape analysis is a set of shape descriptors thatcharacterise either the topology, the specific shape features or both.

In order to determine the orientation of an object in a medical image,e.g. the thorax side of the breast mass, shape analysis techniques areused to describe the topology and characteristics of the object in theimage. The shape of an object determines the extent of the object in theimage, which is a binary image, and the spatial distribution of graylevels inside the object's extent. A shape analysis therefore departsfrom a shape representation, from which shape descriptors arecalculated. Shape representation methods result in a non-numericrepresentation of the original shape capturing the importantcharacteristics of the shape (importance depending on the application).Shape description methods refer to methods that result in a numericdescriptor of the shape, generated by calculating a shape descriptorvector (also called a feature vector). The goal of description is touniquely characterise the shape using its descriptor vector, independentof the shape's position, orientation and size. Conversely, the processof reduction of a shape to its canonical form that is invariant totranslation, rotation and scale, assumes that the actual shape'sposition, orientation and size are determined.

In order to be able to align the breast's shape with the correctassociated image border, it must be determined with which imageborder(s) the breast as a whole is aligned.

In the context of digital mammography, the input to the shape analysisproblem as outlined before, is either a binary representation of theextent of the breast's shape, or a discretely distributed massrepresentation, in which each pixel is attached a mass in the pixel'scenter, the magnitude of the mass being equal to its gray value. Thesegmentation procedure can be performed by prior art techniques andeither outputs a binary image, representing the silhouette of thebreast, or the contour outline, representing the location of thebreast's transition to the direct exposure region. Such prior arttechniques are based on thresholding (such as a technique disclosed inEuropean patent application EP 887 769) or region growing.

Although they are area measures, gray value distribution measures suchas histogram-based statistics (called first order statistics) or localtexture measures (called second and higher-order statistics such asco-occurrence measures) are insufficient to characterize the globalspatial distribution of the anatomy in the radiographic image. Histogrammeasures are inadequate because the spatial information is lost. Texturemeasures based on co-occurrence measures are suitable for description oflocal gray value appearance within the breast mass, but thecharacterization step must be followed by a texture segmentation toprovide the location of the breast tissue in a mammogram. As theappearance of breast tissue may be very diverse, multiple measures willbe needed to characterize the full spectrum of breast appearance. Hence,these prior art methods are therefore inadequate to describe shapeorientation adequately. Therefore, spatial analysis of the breast regionby the general method of moments will be considered in the first part.Equivalently, the spatial distribution of the breast mass, representedand described by the breast-direct exposure region boundary, isaddressed in the second part. Hybrid methods combining both region andcontour analysis may be considered also.

Two basic approaches for constructing shape orientation measures havebeen implemented in the context of the present invention.

Region-Based Shape Orientation Measures

Region Representation

In its simplest form, a region may be viewed as a grouping or collectionof pixels belonging to an entity having a problem-specific semantic(e.g. all pixels belonging to an object part). At a higher level ofabstraction, a region may be described by its decomposition in smallerprimitive forms (such as polygons, or quadtrees). A region may also bedescribed by its bounding region such as the Feret box, the minimumenclosing rectangle or the convex hull. Finally, a region may berepresented by its internal features such as its skeleton, or arun-length representation.

Cartesian Moments

The two-dimensional Cartesian moment m_(pq) of order p+q of a digitalimage ƒ(x,y) is defined as

$m_{pq} = {\sum\limits_{x}{\sum\limits_{y}{x^{p}y^{q}{{f( {x,y} )}.}}}}$

The origin with respect to which x and y are defined is important. Inthe context of the present invention, the x and y coordinate axes of aright-handed coordinate system, attached to the upper left pixel of theimage, are defined to coincide with the leftmost column and uppermostrow of the image respectively.

Moment-based shape description is information-preserving, in that themoments m_(pq) are uniquely determined by the function ƒ(x,y) and viceversa the moments m_(pq) are sufficient to accurately reconstruct theoriginal function ƒ(x,y).

The zero^(th) order moment m₀₀ is equal to the shape area, assuming thatƒ(x,y) represents a binary-valued silhouette segmentation with value 1within the shape (i.c. the breast) and value 0 outside the shape (i.c.the direct exposure region). When ƒ(x,y) represents the original grayvalue image, m₀₀ equals the sum of gray values in the image.Alternatively, ƒ(x,y) may also represent derivatives of the gray valuefunction (e.g. first order edge gradient), so that e.g. high gradientareas contribute more than constant gray value areas.

First-order and higher order moments weight the silhouette function orgray value function by the spatial coordinate. Hence, they are usefuldescriptors to describe the spatial distribution of mass inside theshape. For positive values of p or q, pixels with larger x or ycoordinate with respect to their reference origin are weighted more thanpixels with smaller coordinate value. Conversely, for negative values ofp or q, pixels nearer to the x or y reference axis respectively havehigher contribution to the moment value. Moments with p<0 or q<0 arecalled inverse moments. The magnitude (|p| or |q|) controls the ratewith which the influence of pixels farther away from their origin ortheir respective coordinate axes increases or decreases.

The summation area in computing the moment sums may be confined to oneor more image regions obtained by segmentation. However, thesegmentation may be implicit in that pixels with low gray value ƒ(x,y)have less influence and hence are implicitly ignored in the moment sum.This implicit segmentation of direct exposure area may be used in thetask of detecting the thorax side in mammograms in that pixels of thedirect exposure area have low gray value; hence their contribution tothe moment sum is negligible compared to the contribution of the breastmass pixels. The moment m_(pq) may therefore be obtained by includingall image pixels in the sum, without explicitly segmenting the breastmass.

Moments of Projections

Two-dimensional or area-based moments may be reduced to one-dimensionalmoments by projecting the gray value image onto one axis. The moments ofthe projection are one-dimensional moments of the projection function.The projection direction may for example be

-   -   parallel to the coordinate axes (e.i. integrated in columns,        which is projection parallel to the x-axis, or integrated in        rows, which is projection parallel to the y-axis), reducing the        general moment equation to

${m_{p} = {\sum\limits_{x}{\sum\limits_{y}{x^{p}{f( {x,y} )}}}}},{m_{q} = {\sum\limits_{x}{\sum\limits_{y}{y^{q}{f( {x,y} )}}}}},$

-   -    For p>0 and q>0, this descriptor has small values in cases        where the largest gray values are concentrated along or nearby        the x-axis resp. the y-axis. The opposite effect can be achieved        using negative p or q, yielding the so-called inverse moments.        Pixels for which x=0, or y=0 are excluded from the summation        when computing inverse moments.    -    The breast mass shape in a RCC or LCC view for example may        approximately be described by a circle halve, touching an image        border along its chord. Consequently, when the gray value mass        pertaining to the breast shape is nearby the image border        corresponding to the x-axis, the associated inverse moment will        have higher values than the inverse moment with respect to the        parallel juxtaposed image border, or with respect to any of the        two remaining perpendicular borders corresponding to the y-axis        direction.    -   radial (e.i. the image is integrated on concentric circles,        yielding the radius as the independent variable).

${m_{s} = {\sum\limits_{x}{\sum\limits_{y}{r^{s}{f( {x,y} )}}}}},\mspace{40mu}{r = \sqrt{x^{2} + y^{2}}}$

-   -    This descriptor has small values in cases where the largest        gray value pixels are along or nearby the origin of the        coordinate system. The opposite effect can be achieved using        negative values for s. The pixel at the origin for which r=0        must be excluded in the summation for the inverse moment.    -   parallel to other axes, e.g. parallel to the main diagonal

${m_{k} = {\sum\limits_{x}{\sum\limits_{y}{( {x - y} )^{k}{f( {x,y} )}}}}},$

-   -    This descriptor has small values in cases where the largest        gray value pixels are along or nearby the principal diagonal.        The opposite effect can be achieved using the inverse moment

${m_{- k} = {\sum\limits_{x}{\sum\limits_{y}\frac{f( {x,y} )}{( {x - y} )^{k}}}}},{x \neq y}$

Instead of being computed with respect to axes related to the Cartesianimage coordinate system, they may be computed with respect to axesintrinsic to the object, such as principal axes with respect to whichthere are minimum and maximum second-order moments.

Examples of determining the orientation of the breast mass in CC viewsare illustrated in FIG. 2, where a homogeneous mass distribution insidethe shape is assumed.

A.

$m_{q} = {\sum\limits_{x}{\sum\limits_{y}{y^{q}{f( {x,y} )}}}}$is minimal if q>0 and the object is situated close the x-axis or maximalif q<0 and the object is like-wise situated close to the x-axis.

B.

$m_{p} = {\sum\limits_{x}{\sum\limits_{y}{x^{p}{f( {x,y} )}}}}$is minimal if p>0 and the object is situated close to the y-axis ormaximal if p<0 and the object is like-wise situated close to the y-axis.

C.

$m_{q}^{\prime} = {\sum\limits_{x}{\sum\limits_{y}{( {c - y} )^{q}{f( {x,y} )}}}}$wherein c represents the number of columns is minimal if q>0 and theobject is situated nearby the juxtaposed image border parallel to thex-axis and maximal if the object is like-wise situated nearby thejuxtaposed image border parallel to the x-axis but q<0. This situationis obtained e.g. by reflecting (flipping) the image of configuration Aaround the image-centred vertical, or by rotating 180 degrees the imageof configuration A around the image centre.

D.

$m_{p}^{\prime} = {\sum\limits_{x}{\sum\limits_{y}{( {r - x} )^{p}{f( {x,y} )}}}}$with r representing the number of rows is minimal if p>0 and the objectis situated nearby the juxtaposed image border parallel to the y-axisand maximal if the object is situated nearby the juxtaposed image borderparallel to the y-axis but p<0. This situation is obtained e.g. byreflecting (flipping) the image of configuration B around theimage-centred horizontal, or by rotating 180 degrees the image ofconfiguration B around the image centre.

Moments with Respect to Points

Moments can be expressed to points whereby the gray value (or binaryquantized value) is weighted with distance to a point. In contrast tothe general moment generating function where x and y coordinates areseparated, the topology information x and y may be combined in a singlegeometric measure, which can for example be distance to a given point,raised to a suitable power. The moment generating function then becomesa radial projection, with lines of equal contribution (for a constantgray value) being concentric circles around the given point (x_(i),y_(i)).

${m_{s} = {\sum\limits_{x}{\sum\limits_{y}{r^{s}{f( {x,y} )}}}}},\mspace{40mu}{r = \sqrt{( {x - x_{i}} )^{2} + ( {y - y_{i}} )^{2}}}$

Several anchor points (x_(i),y_(i)), i=1 . . . N may thus be consideredand the resulting image moments may be compared with respect to eachother, to determine the anchor point around which the gray value masstopologically is most concentrated. By suitably choosing the set ofanchor points, a topological analysis of the image may be conducted inview of the problem, which is one of orientation detection.

The loci of equal geometrical contribution (considering the gray valueconstant) to any pair of points of the set (x_(i),y_(i)), i=1 . . . N isgiven by the set of intersection of corresponding circles (with equalradius) around each of the two points of the pair. These loci form astraight line, called the perpendicular bisector. For each pixel in thehalf plane of the line, the distance to the representative point in itsassociated half plane of the line is smaller than the distance to thepoint in the other half plane. Considering now a triple of points,forming a triangle, the perpendicular bisectors may be drawn in betweenany two vertices of the triple, and it is a known property of planargeometry that these bisectors meet in a common point. The complete setof points (x_(i),y_(i)), i=1 . . . N may be tessellated in a group ofcontiguous triangles, none of them overlapping and the ensemble of whichcovers the plane (or part of the plane) completely. This procedure iscalled triangulation. The process of bisecting may now be performed onany of the constituent triangles, and the result of this operation is aminimum-distance tessellation of the plane into polygonally shaped cellsC_(i), the ensemble being called a Voronoi diagram. Each cell containsexactly one representative of the original set of points (x_(i),y_(i)),i=1 . . . N. This diagram has the property that the distance of a pointin a certain cell is nearer to the representative point of this cellthan to any other point of the original point set. Each cell thusrepresents the locus of proximity of pixels (x,y) in the plane w.r.t.the set of points (x_(i),y_(i)),i=1 . . . N.

The choice of points in the point set (x_(i),y_(i)), i=1 . . . N isimposed by the problem at hand. For mammography orientation detection,suitable points are the midpoint of the thorax breast side of the CCview, which may be seen to coincide approximately with midpoint of theassociated image border. For the MLO view, the breast is diagonallyspread out between the compressor plates, Therefore, in contrast to theCC view; there is also image information in one of the four imagecorners. Hence, image corner points are suitable anchor points also.Depending on the subset taken from the combined set of 4 bordermidpoints and 4 corner points, different Voronoi tessellations areobtained, each of which having interesting topological properties.

Each of the Voronoi cells C_(i) in a Voronoi tessellation represents animage area, all pixels of which are topologically closer to point(x_(i),y_(i)) than to any other point in the point set (x_(i),y_(i)),i=1 . . . N. Moments of the type m_(s) may now be computed to measurethe distribution of the gray values of pixels inside the cell C_(i) toits representative cell point (x_(i),y_(i)). When larger gray values arelocated farther from (x_(i),y_(i)), moments with positive values for swill be larger than moments of a distribution where pixels with largergray values are nearer to (x_(i),y_(i)). The reverse holds for inversemoments obtained by negative values for s in that they measureconcentration of gray value mass around (x_(i),y_(i)). In spite of itssimplicity, the zero-order moment m_(s=0) is also particularly useful.Since it is the sum of gray values inside the Voronoi cell, the ensemblem₀(i) of all Voronoi cells is representative for the topologicaldistribution of gray value mass in the image. When the image isbinarized, this zero-order moment is representative for the topologicaldistribution of the image object, for it measures the image area of theimage object contained in each Voronoi cell. The usefulness ofzero-order moment of binary images may further be normalized bycomputing the measure m₀(i)/A(i), where A(i) represents the area of theVoronoi cell C_(i). This fractional measure represents the fill factorof cell C_(i); hence it measures how an object is topologicallydistributed in the image plane. A weight may further be attached to eachcell moment, e.g. the reciprocal of the cell's relative area (relativeto the total image area), to obtain equal importance of each cell incomparison between cells, irrespective of their absolute size.

Minimum distance tessellations may be constructed for other geometricalobjects, such as lines, in a similar way.

Examples of determining the orientation of the breast mass in MLO viewsis given in FIG. 3.

-   -   E. m_(s) with (x_(i),y_(i))=(0,0) is minimal if s>0 and the        object is situated close to the upper-left image corner or        maximal if s<0 and the object is like-wise situated close to the        upper-left image corner.    -   F. m_(s) with (x_(i),y_(i))=(0,c) wherein c represents the        number of columns is minimal if s>0 and the object is situated        close to the upper-right image corner or maximal if s<0 and the        object is like-wise situated close to upper-right corner.    -   G. m_(s) with (x_(i),y_(i))=(r,0) wherein r represents the        number of rows is minimal if s>0 and the object is situated        close to the lower-left image corner and maximal if the object        is like-wise situated close to the lower-left image corner but        s<0

H. m_(s) with (x_(i),y_(i))=(r,c) is minimal if s>0 and the object issituated close to the lower-right image corner and maximal if the objectis like-wise situated close to the lower-right image corner but s<0.

Curve-Based Shape Orientation Measures

Curve Representation

A curve or contour may in its simplest form be represented by the set of(possibly chained) contour pixels. At a higher level, the curve may beapproximated in primitive forms such as a collection of approximatingline segments (a polygonal representation, alternatively represented bythe corner intersections), circle arcs, elliptical arcs, syntacticprimitives, B-splines, Snakes and active contours, or multiscaleprimitives. Finally, a curve may be represented parametrically, forexample as a two-component vector γ(t)={x(t),y(t)} for a plane curve, oras a complex signal u(t)=x(t)+jy(t), a chain code or a run-length code.

Moment Measures Based on Boundaries of Binary Silhouettes

For binary silhouette images, moment measures based on the contour ofthe binary object are essential equivalent to moments computed from theinterior of the shape (the occupancy array). The number of boundarypixels is generally proportional to the square root of the total numberof pixels inside the shape. Therefore, representing a shape by itsboundary is more efficient than representing the shape with an occupancyarray. This advantage of faster computation becomes even greater whenthe shape is polygonal, or with many straight segments along itsboundary. The moments with respect to a reference point may then becomputed by summing the moments of triangles formed by the twoneighbouring corner points spanning a line segment of the 2D polygonal(or polygonal approximated) shape and the reference point. The momentswith respect to a (in general arbitrarily oriented) reference line arecomputable as the sum of moments of trapezoids formed by the two cornerpoints spanning the line segment of the 2D shape and the normalprojections of those points on the reference line. Said elementarymoments based on a triangle and a trapezoid will only depend on thevertex coordinates.

Extension to 3D Object Orientation Detection

It will be clear that moments in 3 dimensions can be used to determinethe 3D orientation of a 3D object in a 3D medical image. In this respectspecialisations of the 3D moment generating function may be generated byprojecting the 3D medical image onto planes or lines or by consideringradial projection around points.

1. A method of detecting the orientation of a radiographic imagerepresented by a digital signal representation comprising: calculating,via a medical computer system, mathematical moments of said digitalsignal representation relative to different reference entities; andobtaining, via the medical computer system, a decision on theorientation of said radiographic image on the basis of an extreme valuecomprising one of a maximum and a minimum of the calculated moments,wherein said moments are one-dimensional moments obtained by projectingthe digital signal representation of said image onto a predefined axis.2. The method according to claim 1 wherein said axis is parallel to oneof the boundaries of said image.
 3. A method of detecting theorientation of a radiographic image represented by a digital signalrepresentation comprising: calculating, via a medical computer system,mathematical moments of said digital signal representation relative todifferent reference entities; and obtaining, via the medical computersystem, a decision on the orientation of said radiographic image on thebasis of an extreme value comprising one of a maximum and a minimum ofthe calculated moments, wherein said digital signal representation is afunction of at least one derivative of an original digital signalrepresentation.
 4. The method according to claim 3 wherein saidderivative is the first order edge gradient.
 5. A method of detectingthe orientation of a radiographic image represented by a digital signalrepresentation comprising: calculating, via a medical computer system,mathematical moments of said digital signal representation relative todifferent reference entities; and obtaining, via the medical computersystem, a decision on the orientation of said radiographic image on thebasis of an extreme value comprising one of a maximum and a minimum ofthe calculated moments, wherein collimation area are excluded from saiddigital signal representation.
 6. A method of detecting the orientationof a radiographic image represented by a digital signal representationcomprising: calculating, via a medical computer system, mathematicalmoments of said digital signal representation relative to differentreference entities; and obtaining, via the medical computer system, adecision on the orientation of said radiographic image on the basis ofan extreme value comprising one of a maximum and a minimum of thecalculated moments, wherein direct exposure area are excluded from saiddigital signal representation.
 7. The method according to claim 6wherein a moment is a cartesian moment which moment weights the digitalsignal representation by a function of at least one spatial coordinate xor y.
 8. The method according to claim 7 wherein a moment is calculatedwith respect to a cartesian co-ordinate system the axes of which aresubstantially parallel to the boundaries of said image.
 9. The methodaccording to claim 6 wherein said moments are two-dimensional moments.10. The method according to claim 6 wherein a moment is generated withrespect to at least one predefined point.
 11. A non-transitory computerreadable medium comprising computer executable program code adapted tocarry out the steps of claim
 7. 12. A non-transitory computer readablemedium comprising computer executable program code adapted to carry outthe steps of claim
 8. 13. A non-transitory computer readable mediumcomprising computer executable program code adapted to carry out thesteps of claim
 9. 14. A non-transitory computer readable mediumcomprising computer executable program code adapted to carry out thesteps of claim
 1. 15. A non-transitory computer readable mediumcomprising computer executable program code adapted to carry out thesteps of claim
 2. 16. A non-transitory computer readable mediumcomprising computer executable program code adapted to carry out thesteps of claim
 10. 17. A non-transitory computer readable mediumcomprising computer executable program code adapted to carry out thesteps of claim
 3. 18. A non-transitory computer readable mediumcomprising computer executable program code adapted to carry out thesteps of claim
 4. 19. A non-transitory computer readable mediumcomprising computer executable program code adapted to carry out thesteps of claim
 5. 20. A non-transitory computer readable mediumcomprising computer executable program code adapted to carry out thesteps of claim 6.